We need some preparations on the multiplications of tensors and the related terminology and notations before we introduce the Grassmann tensor. There are mainly three kind of multiplications of tensors: the outer product (also called tensor product), contractive (mode) product, and the t-product defined on 3-order tensors. We will introduce the first two in this paper and generalize the outer-product of two tensors. For the t-product of two 3-order tensors, we refer the reader to [1]}, [2]}, [3]}.
